Algorithms for constructing of decision trees

Moshkov, Mikhail

doi:10.1007/3-540-63223-9_132

Cited by 9 publications

(4 citation statements)

References 3 publications

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“…In Moshkov (2007); Moshkov and Chikalov (2000) infinite sets of attributes (so-called restricted information systems) were studied for each of which the number of separable subtables in decision tables over the considered set of attributes is bounded from above by a polynomial on the number of attributes in the table. For decision tables over such set of attributes, the time complexity of each of the algorithms A 1 , A 3 , and A 4 is bounded from above by a polynomial on the size of the input table.…”

Section: On Complexity Of Algorithmsmentioning

confidence: 99%

Bi-criteria optimization problems for decision rules

et al. 2018

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We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems -minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion -we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria -we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.

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Section: On Complexity Of Algorithmsmentioning

confidence: 99%

Bi-criteria optimization problems for decision rules

et al. 2018

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“…This algorithm is based on dynamic programming approach [20], [5], and the complexity of this algorithm in the worst case is exponential.…”

Section: A Dynamic Programming Algorithmmentioning

confidence: 99%

Minimizing Size of Decision Trees for Multi-label Decision Tables

Azad¹,

Moshkov²

2014

Annals of Computer Science and Information Systems

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Abstract-We used decision tree as a model to discover the knowledge from multi-label decision tables where each row has a set of decisions attached to it and our goal is to find out one arbitrary decision from the set of decisions attached to a row. The size of the decision tree can be small as well as very large. We study here different greedy as well as dynamic programming algorithms to minimize the size of the decision trees. When we compare the optimal result from dynamic programming algorithm, we found some greedy algorithms produce results which are close to the optimal result for the minimization of number of nodes (at most 18.92% difference), number of nonterminal nodes (at most 20.76% difference), and number of terminal nodes (at most 18.71% difference).

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“…In order to select the most relevant partitioning, the learning algorithm changes the order of the attributes for each input decision relation so that the most relevant attributes are selected first, and possibly the less relevant [50] ignored. As an example of such a recursive algorithm that learns a decision function df from a decision relation DR, we take commonly used C4.5 algorithm [65], which is outlined in the Algorithm 2.…”

Section: Decision Interpolationmentioning

confidence: 99%

Decisions: Algebra and Implementation

Danylenko

Lundberg

Löwe

2011

Machine Learning and Data Mining in Pattern Recognition

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Processing decision information is a constitutive part in a number of applications in Computer Science fields. In general, decision information can be used to deduce the relationship between a certain context and a certain decision. Decision information is represented by a decision model that captures this information. Frequently used examples of decision models are decision tables and decision trees. The choice of an appropriate decision model has an impact on application performance in terms of memory consumption and execution time. High memory expenses can possibly occur due to redundancy in a decision model; and high execution time is often a consequence of an unsuitable decision model. Applications in different domains try to overcome these problems by introducing new data structures or algorithms for implementing decision models. These solutions are usually domain-specific and hard to transfer from one domain to another.Different application domains of Computer Science often process decision information in a similar way and, hence, have similar problems. We should thus be able to present a unifying approach that can be applicable in all application domains for capturing and manipulating decision information. Therefore, the goal of this thesis is (i) to suggest a general structure (Decision Algebra) which provides a common theoretical framework that captures decision information and defines operations (signatures) for storing, accessing, merging, approximating, and manipulating such information along with some general algebraic laws regardless of the used implementation. Our Decision Algebra allows defining different construction strategies for decision models and data structures that capture decision information as implementation variants, and it simplifies experimental comparisons between them.Additionally, this thesis presents (ii) an implementation of Decision Algebra capturing the information in a non-redundant way and performing the operations efficiently. In fact, we show that existing decision models that originated in the field of Data Mining and Machine Learning and variants thereof as exploited in special algorithms can be understood as alternative implementation variants of the Decision Algebra by varying the implementations of the Decision Algebra operations. Hence, this work (iii) will contribute to a classification of existing technology for processing decision information in different application domains of Computer Science.

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Algorithms for constructing of decision trees

Cited by 9 publications

References 3 publications

Bi-criteria optimization problems for decision rules

Bi-criteria optimization problems for decision rules

Minimizing Size of Decision Trees for Multi-label Decision Tables

Decisions: Algebra and Implementation

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